1. Field of the Invention
The present invention is directed to an automatic frequency control (AFC) loop multipath combiner for a RAKE receiver, and more particularly, to an AFC combiner which removes the Doppler frequency offsets from all the RAKE fingers.
2. Discussion of the Prior Art
Typically in terrestrial communication, a receiver receives a transmitted signal which has traveled through a direct path and indirect paths. Propagation through the indirect paths, referred to as multipath propagation, results from the transmitted signal being reflected and refracted by surrounding terrain. The multipath signals traveling through the indirect paths undergo frequency and time offsets.
To exploit the energy in the multiple components of multipath propagation of a transmitted signal, a RAKE receiver is used which has multiple parallel demodulators for receiving different multipath components of the transmitted signal. Each multipath component demodulator is called a "finger" of the RAKE receiver. The RAKE receiver identifies and acquires the multiple components of multipath propagation with the aid of a pilot signal. As well known to those skilled in the art, a RAKE receiver collects and combines the energy from the distinct paths.
Typically a RAKE receiver uses an automatic frequency control (AFC) loop for initial frequency acquisition and Doppler frequency adjustment of the received signal which has been disturbed by noise and multipath. The Doppler frequency offsets of the disturbed or faded signals are often unknown. A balanced discrete quadri-correlator or cross-product automatic frequency control (CP-AFC) loop structure is used to obtain the unknown frequency offsets.
In the CP-AFC loop, the unknown frequency offset is obtained through differentiation as will be described in connection with equations (5) and (7). To derive the CP-AFC, consider an optimal phase estimator structure 10 shown in FIG. 1. As shown in FIG. 1, a received signal y(t) is provided to two mixers 12, 14, which respectively receive locally oscillating signals 16, 18 having a 90.degree. phase difference. These two signals are provided from a local oscillator, such as a voltage controlled oscillator (VCO) 20, where one of the signals passes through a 90.degree. phase shifter 22. The outputs of the two mixers 12, 14 are provided to two integrators (or lowpass filters) 32, 34, respectively.
The received signal y(t) is expressed by equation (1): EQU y(t)=2A sin[.omega.t+(.omega.-.omega.)t+.theta.]+n(t) (1)
where:
.omega. is the frequency of the local oscillator 20; PA1 .omega. is the frequency of the received signal y(t); PA1 .theta. is an unknown constant carrier phase; and PA1 n(t) is noise.
Combining the frequency difference term (.omega.-.omega.) with the unknown constant carrier phase e into one unknown time variant phase .theta.(t), equation (1) is rewritten as equation (2): EQU y(t)=2A sin[.omega.t+.theta.(t)]+n(t) (2)
In the noise free case, the outputs of the integrators or lowpass filters 32, 34 are given by equations (3) and (4): EQU y.sub.c (t)=A cos.theta.(t) (3)
and EQU y.sub.s (t)=A sin.theta.(t) (4)
As seen from equations (3) and (4), the purpose of the lowpass filters (LPFs) 32, 34 is to suppress the double frequency term resulting from the product of y(t) with the locally oscillating signals 16, 18. The difference (.omega.-.omega.) between the received signal frequency (.omega.) and the local oscillator frequency (.omega.) is given by equation (5): ##EQU1##
where .theta.(t) is the output of the phase estimator 10 shown in FIG. 1.
Using the identity shown in equation (6): ##EQU2##
equation (5) can be expressed as equation (7): ##EQU3##
Because of the differentiator in equation (5), a CP-AFC structure realization of equation (5) is also known as the differentiator AFC. In the discrete domain, the differentiator AFC structure can be easily derived by replacing the derivative dy(t)/dt at time t=n.DELTA.T by the expression shown in equation (8): ##EQU4##
where .DELTA.T represents the sampling period. The analog differentiator dy(t)/dt has a system transfer function H(s)=s, whereas the discrete system has the transfer function given by equation (9) which can be deduced from equation (8): ##EQU5##
Consequently, the mapping between the analog and the discrete domains is governed by equation (10): ##EQU6##
Note that the mapping in equation (10) is only suitable for lowpass and bandpass filters having relatively small resonant frequencies.
In order to derive the structure for the discrete-time differentiator AFC, equation (8) is substituted into equation (7) to yield equation (11): EQU y'.sub.s (t)y.sub.c (t)-y'.sub.c (t)y.sub.s (t).apprxeq.[1/.DELTA.T][y.sub.s (n-1)y.sub.c (n)-y.sub.c (n-1)y.sub.s (n)] (11)
The realization of equation (11) is a discrete differentiator AFC (or CP-AFC) loop structure depicted in FIG. 2, which will be described later.
The relation in equation (11) can be further expressed as equation (12): EQU y'.sub.s (t)y.sub.c (t)-y'.sub.c (t)y.sub.s (t).apprxeq.[1/.DELTA.T]sin(.DELTA.T.DELTA..omega.) (12)
where .DELTA..omega.=.omega.-.omega..
When operating in the linear region (i.e., theoretically .DELTA..omega..DELTA.T&lt;&lt;1)), the error signal D(.omega.-.omega.) is directly proportional to the difference between the received signal and local oscillator frequencies. The relationship is no longer linear when .DELTA..omega. becomes large.
FIG. 2 shows a typical cross-product (CP) AFC 100 having a frequency discriminator (FD) 110 which is a realization of the expression shown in equation (11). Similar to the phase estimator 10 of FIG. 1, the received signal y(t) is provided to the two mixers 12, 14 for down conversion using locally oscillated signals 16, 18 which are 90.degree. apart and provided from the VCO 20, where one signal is phase shifted by a 90.degree. phase shifter. For clarity, the 90.degree. phase shifter 22, shown in FIG. 1, is omitted from FIG. 2.
The down-converted signals pass through respective analog-to-digital A/D converters 120, 125, integrators 130, 135, and dump or low-pass filters 140, 145. The output signals of the dump filters 140, 145 are indicated as y.sub.s and y.sub.c, respectively, which are the input signals to the frequency discriminator 110. The first signal y.sub.s passes though a first delay element 150 and a first mixer or multiplier 155. Similarly, the second signal y.sub.c passes though a second delay element 160 and a second mixer or multiplier 165. The first signal y.sub.s is also provided to the second mixer 165, while the second signal y.sub.c is also provided to the first mixer 155.
The outputs of the two mixers 155, 165 are provided to a combining circuit 170, such as a substractor or an adder, where one of the adder inputs 170 is inverted to result in subtraction of its two inputs. The output of the adder 170 is the difference signal shown on the left side of equations (11) and (12). This difference signal from the adder 170 is an estimate of the frequency error.
The difference signal from the adder 170 is provided to other circuits for processing. In addition, the difference signal from the adder 170 is fed back to the VCO 20 through a loop filter 175 and a digital-to-analog (D/A) converter 180. The output of the loop filter 175 is an estimate of the frequency offset. The D/A converter 180 converts its digital input to an analog signal which is used to adjust the frequency of oscillation of the VCO 20.
The output of the VCO 20 is then fed back to either the frequency discriminator (FD) 110 or to intermediate frequency (IF) mixers to form what is referred to as a short loop or a long loop, respectively. In FIG. 2, the output of the VCO is fed back to the mixers 12 and 14, where the 90.degree. phase shifter 22 (FIG. 1) is provided between the VCO 20 and the mixer 12 as described in connection with FIG. 1.
For simplicity, short and long loops are not distinguished in FIG. 2, since FIG. 2 shows only one set of mixers 12, 14 which convert the received RF signal to baseband signals which are provided to the A/D converters 120, 125. However, typically two sets of mixers are provided; IF mixers which convert the received radio frequency (RF) signal to an intermediate frequency (IF) signals 90.degree. apart; and zero IF mixers which convert the IF signals to the baseband signals for input to the A/D converters 120, 125. A short loop connects the VCO to the IF mixers and a long loop connects the VCO to the zero IF mixers. Typically, an RF filter is provided between the IF and zero IF mixers.
The mixers 155, 165 of the frequency discriminator (FD) 110 play the role of correlation detectors. That is, the received signal y(t) is cross-correlated with signals 18, 16 from the VCO 20 and phase shifter 22 (FIG. 1), namely, with sin (.omega.t) and cos(.omega.t). The results of this cross-correlation are the respective outputs sin[(.omega.-.omega.t)] and cos[(.omega.-.omega.t)] from the two mixers 14, 12. This is the noise free case. In the presence of noise, however, the sine and cosine terms are contaminated with an additive broadband noise term, which at low signal-to-noise-ratio (SNR) tends to dominate the original sinusoidal signals. Note that the desired signals (sinusoids) are very close to the baseband signal when compared to the overall bandwidth (BW) of the noise.
The signals provided from the mixers 12, 14 are digitized by the A/D converters 120, 125. In order to improve the SNR, the digitized signals are then passed through integrate-and-dump or appropriate low pass filters 130, 140 and 135, 145, respectively. This smooths out the noise. Next, the filtered signals are passed through the differentiator circuit or frequency discriminator 110 which comprises the two delays 150, 160, the two multipliers 155, 160, and the adder 170. The output of the adder 170 is the difference signal which is fed back to the VCO as described above.
In CDMA IS95 based systems, during the pilot acquisition stage, the mismatch between the frequency .omega. of the received signal y(t), and the frequency .omega. of the local oscillator 20 can be on the order of several Khz, such as up to 6 KHz or more, depending on the oscillator frequency. This frequency mismatch is due to the Doppler frequency shift. At this stage, the AFC 100 is used to correct for the frequency mismatch. During steady state, the AFC 100 attempts to track the Doppler frequency shift. For a carrier frequency between 800 MHZ and 900 MHZ, the Doppler shift is typically around 90 Hz. For personal communication system (PCS) applications, the Doppler shift can be as high as 300 Hz.
In a conventional Rake receiver, an AFC can operate on the combination of frequency offsets obtained from various fingers by placing various frequency detectors on each finger. This method results in a frequency offset estimate which is the average of frequency offset estimates present in the various Rake fingers. However, in this method, only the weighted average frequency offset is removed from each path. The result is to leave each finger with a frequency offset error equal to the difference between the center frequency of the received signal multipath and the estimated average frequency. This, in turn, could also introduce additional offsets and errors depending on the strength of the pilots present in each finger, thus reducing the performance of the system.
In conventional Rake receivers with AFC circuits, the frequency offsets remain in one or more of the Rake fingers causing additional degradation to the system's performance. Accordingly, there is a need for a Rake receiver with AFC circuits that remove the frequency offsets from all the Rake fingers.